Problem: Divide the following complex numbers: $\dfrac{3(\cos(\frac{11}{12}\pi) + i \sin(\frac{11}{12}\pi))}{\cos(\frac{2}{3}\pi) + i \sin(\frac{2}{3}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $3(\cos(\frac{11}{12}\pi) + i \sin(\frac{11}{12}\pi))$ ) has angle $\frac{11}{12}\pi$ and radius 3. The second number ( $\cos(\frac{2}{3}\pi) + i \sin(\frac{2}{3}\pi)$ ) has angle $\frac{2}{3}\pi$ and radius 1. The radius of the result will be $\frac{3}{1}$ , which is 3. The angle of the result is $\frac{11}{12}\pi - \frac{2}{3}\pi = \frac{1}{4}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{1}{4}\pi$.